Wikispaces>Andrew_Heathwaite |
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| <h2>IMPORTED REVISION FROM WIKISPACES</h2>
| | The 47-odd-limit. Whoa. |
| This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br>
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| : This revision was by author [[User:Andrew_Heathwaite|Andrew_Heathwaite]] and made on <tt>2013-10-25 18:19:31 UTC</tt>.<br>
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| : The original revision id was <tt>463187734</tt>.<br>
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| : The revision comment was: <tt></tt><br>
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| The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.<br>
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| <h4>Original Wikitext content:</h4>
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| <div style="width:100%; max-height:400pt; overflow:auto; background-color:#f8f9fa; border: 1px solid #eaecf0; padding:0em"><pre style="margin:0px;border:none;background:none;word-wrap:break-word;white-space: pre-wrap ! important" class="old-revision-html">The 47-limit. Whoa.
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| Here is a list of the intervals within the octave belonging to the 47-odd limit -- that is, intervals between 1/1 and 2/1 which contain no odd numbers greater than 47. It is organized by [[interval category]] according to the Schulter System outlined in [[http://www.bestii.com/~mschulter/IntervalSpectrumRegions.txt|Regions of the Interval Spectrum]]. | | Here is a list of the intervals within the octave belonging to the 47-[[Odd_limit|odd limit]] -- that is, intervals between 1/1 and 2/1 which contain no odd numbers greater than 47. It is organized by [[interval_category|interval category]] according to the Schulter System outlined in [http://www.bestii.com/~mschulter/IntervalSpectrumRegions.txt Regions of the Interval Spectrum]. |
|
| |
|
| ==Pure Unison (0 cents)== | | ==Pure Unison (0 cents)== |
| ||~ ratio ||~ cents value ||
| |
| || 1/1 || 0 ||
| |
|
| |
|
| ==Commas (0-30 cents)== | | {| class="wikitable" |
| | |- |
| | ! | ratio |
| | ! | cents value |
| | |- |
| | | | 1/1 |
| | | | 0 |
| | |} |
| | |
| | ==Commas (0-30 cents)== |
| None within the 47-odd limit. | | None within the 47-odd limit. |
|
| |
|
| ==Dieses (30-60 cents)== | | ==Dieses (30-60 cents)== |
| ||~ ratio ||~ cents value ||~ prime limit || | | |
| || 48/47 || 36.448 || 47 ||
| | {| class="wikitable" |
| || 47/46 || 37.232 || 47 ||
| | |- |
| || 46/45 || 38.051 || 23 ||
| | ! ratio |
| || 45/44 || 38.906 || 11 || | | ! cents value |
| || 44/43 || 39.800 || 43 ||
| | ! prime limit |
| || 43/42 || 40.737 || 43 || | | |- |
| || 42/41 || 41.719 || 41 || | | | 48/47 |
| || 41/40 || 42.749 || 41 || | | | 36.448 |
| || 40/39 || 43.831 || 13 || | | | 47 |
| || 39/38 || 44.970 || 19 || | | |- |
| || 38/37 || 46/169 || 37 || | | | 47/46 |
| || 37/36 || 47.434 || 37 || | | | 37.232 |
| || 36/35 || 48.770 || 7 || | | | 47 |
| || 35/34 || 50.184 || 17 || | | |- |
| || 34/33 || 51.682 || 17 || | | | 46/45 |
| || 33/32 || 53.273 || 11 || | | | 38.051 |
| || 32/31 || 54.964 || 31 || | | | 23 |
| || 31/30 || 56.767 || 31 || | | |- |
| || 30/29 || 58.692 || 29 || | | | [[45/44]] |
| | | 38.906 |
| | | 11 |
| | |- |
| | | 44/43 |
| | | 39.800 |
| | | 43 |
| | |- |
| | | 43/42 |
| | | 40.737 |
| | | 43 |
| | |- |
| | | 42/41 |
| | | 41.719 |
| | | 41 |
| | |- |
| | | 41/40 |
| | | 42.749 |
| | | 41 |
| | |- |
| | | [[40/39]] |
| | | 43.831 |
| | | 13 |
| | |- |
| | | 39/38 |
| | | 44.970 |
| | | 19 |
| | |- |
| | | 38/37 |
| | | 46/169 |
| | | 37 |
| | |- |
| | | 37/36 |
| | | 47.434 |
| | | 37 |
| | |- |
| | | [[36/35]] |
| | | 48.770 |
| | | 7 |
| | |- |
| | | 35/34 |
| | | 50.184 |
| | | 17 |
| | |- |
| | | 34/33 |
| | | 51.682 |
| | | 17 |
| | |- |
| | | [[33/32]] |
| | | 53.273 |
| | | 11 |
| | |- |
| | | [[32/31]] |
| | | 54.964 |
| | | 31 |
| | |- |
| | | [[31/30]] |
| | | 56.767 |
| | | 31 |
| | |- |
| | | 30/29 |
| | | 58.692 |
| | | 29 |
| | |} |
| | |
| | ==Minor Seconds (60-125 cents)== |
| | |
| | ===Small Minor Seconds (60-80 cents)=== |
| | |
| | {| class="wikitable" |
| | |- |
| | ! ratio |
| | ! cents value |
| | ! prime limit |
| | |- |
| | | 29/28 |
| | | 60.751 |
| | | 29 |
| | |- |
| | | [[28/27]] |
| | | 62.961 |
| | | 7 |
| | |- |
| | | [[27/26]] |
| | | 65.337 |
| | | 13 |
| | |- |
| | | [[26/25]] |
| | | 67.900 |
| | | 13 |
| | |- |
| | | [[25/24]] |
| | | 70.672 |
| | | 5 |
| | |- |
| | | [[24/23]] |
| | | 73.681 |
| | | 23 |
| | |- |
| | | 47/45 |
| | | 75.283 |
| | | 47 |
| | |- |
| | | [[23/22]] |
| | | 76.956 |
| | | 23 |
| | |- |
| | | 45/43 |
| | | 78.706 |
| | | 43 |
| | |} |
| | |
| | ===Middle Minor Seconds (80-100 cents)=== |
| | |
| | {| class="wikitable" |
| | |- |
| | ! ratio |
| | ! cents value |
| | ! prime limit |
| | |- |
| | | [[22/21]] |
| | | 80.537 |
| | | 11 |
| | |- |
| | | 43/41 |
| | | 82.455 |
| | | 43 |
| | |- |
| | | [[21/20]] |
| | | 84.467 |
| | | 7 |
| | |- |
| | | 41/39 |
| | | 86.580 |
| | | 41 |
| | |- |
| | | [[20/19]] |
| | | 88.801 |
| | | 19 |
| | |- |
| | | 39/37 |
| | | 91.139 |
| | | 37 |
| | |- |
| | | [[19/18]] |
| | | 93.603 |
| | | 19 |
| | |- |
| | | 37/35 |
| | | 96.204 |
| | | 37 |
| | |- |
| | | [[18/17]] |
| | | 98.955 |
| | | 17 |
| | |} |
| | |
| | ===Large Minor Seconds (100-125 cents)=== |
| | |
| | {| class="wikitable" |
| | |- |
| | ! ratio |
| | ! cents value |
| | ! prime limit |
| | |- |
| | | 35/33 |
| | | 101.867 |
| | | 11 |
| | |- |
| | | 17/16 |
| | | 104.955 |
| | | 17 |
| | |- |
| | | 50/47 |
| | | 107.121 |
| | | 47 |
| | |- |
| | | 33/31 |
| | | 108.237 |
| | | 31 |
| | |- |
| | | 16/15 = 48/45 |
| | | 111.731 |
| | | 5 |
| | |- |
| | | 47/44 |
| | | 114.189 |
| | | 47 |
| | |- |
| | | 31/29 |
| | | 115.458 |
| | | 31 |
| | |- |
| | | 46/43 |
| | | 116.757 |
| | | 43 |
| | |- |
| | | 15/14 = 45/42 |
| | | 119.443 |
| | | 7 |
| | |- |
| | | 44/41 |
| | | 122.256 |
| | | 41 |
| | |- |
| | | 29/27 |
| | | 123.712 |
| | | 29 |
| | |} |
| | |
| | ==Central or Zalzalian Seconds (formerly Neutral Seconds) (125-170 cents)== |
| | |
| | ===Small Central Seconds (125-135 cents)=== |
| | |
| | {| class="wikitable" |
| | |- |
| | ! ratio |
| | ! cents value |
| | ! prime limit |
| | |- |
| | | 43/40 |
| | | 125.204 |
| | | 43 |
| | |- |
| | | 14/13 = 42/39 |
| | | 128.298 |
| | | 13 |
| | |- |
| | | 41/38 |
| | | 131.549 |
| | | 41 |
| | |- |
| | | 27/25 |
| | | 133.238 |
| | | 5 |
| | |- |
| | | 40/37 |
| | | 134.970 |
| | | 37 |
| | |} |
| | |
| | ===Middle Central Seconds (135-160 cents)=== |
| | |
| | {| class="wikitable" |
| | |- |
| | ! ratio |
| | ! cents value |
| | ! prime limit |
| | |- |
| | | 13/12 = 39/36 |
| | | 138.573 |
| | | 13 |
| | |- |
| | | 38/35 |
| | | 142.373 |
| | | 19 |
| | |- |
| | | 25/23 |
| | | 144.353 |
| | | 23 |
| | |- |
| | | 37/34 |
| | | 146.389 |
| | | 37 |
| | |- |
| | | 12/11 = 36/33 |
| | | 150.637 |
| | | 11 |
| | |- |
| | | 47/43 |
| | | 153.989 |
| | | 47 |
| | |- |
| | | 35/32 |
| | | 155.140 |
| | | 7 |
| | |- |
| | | 23/21 |
| | | 157.493 |
| | | 23 |
| | |- |
| | | 34/31 |
| | | 159.920 |
| | | 31 |
| | |} |
| | |
| | ===Large Central Seconds (160-170 cents)=== |
| | |
| | ====Beginning of Equable Heptatonic Region (160-182 cents)==== |
| | |
| | {| class="wikitable" |
| | |- |
| | ! ratio |
| | ! cents value |
| | ! prime limit |
| | |- |
| | | 45/41 |
| | | 161.161 |
| | | 41 |
| | |- |
| | | 11/10 = 33/30 |
| | | 165.004 |
| | | 11 |
| | |- |
| | | 43/39 |
| | | 169.035 |
| | | 43 |
| | |} |
| | |
| | ====End of Large Central Seconds Region, continuation of Equable Heptatonic Region==== |
| | |
| | {| class="wikitable" |
| | |- |
| | ! ratio |
| | ! cents value |
| | ! prime limit |
| | |- |
| | | 32/29 |
| | | 170.423 |
| | | 29 |
| | |- |
| | | 21/19 |
| | | 173.268 |
| | | 19 |
| | |- |
| | | 52/47 |
| | | 175.021 |
| | | 47 |
| | |- |
| | | 31/28 |
| | | 176.210 |
| | | 31 |
| | |- |
| | | 41/37 |
| | | 177.718 |
| | | 41 |
| | |} |
| | |
| | ====End of Equable Heptatonic Region.==== |
| | |
| | ==Major Seconds (180-240 cents)== |
| | |
| | ===Small Major Seconds (180-200 cents)=== |
| | |
| | {| class="wikitable" |
| | |- |
| | ! ratio |
| | ! cents value |
| | ! prime limit |
| | |- |
| | | 10/9 = 30/27 = 50/45 |
| | | 182.404 |
| | | 5 |
| | |- |
| | | 39/35 |
| | | 187.343 |
| | | 13 |
| | |- |
| | | 29/26 |
| | | 189.050 |
| | | 29 |
| | |- |
| | | 19/17 |
| | | 192.558 |
| | | 19 |
| | |- |
| | | 47/42 |
| | | 194.726 |
| | | 47 |
| | |- |
| | | 28/25 |
| | | 196.198 |
| | | 7 |
| | |- |
| | | 37/33 |
| | | 198.071 |
| | | 37 |
| | |- |
| | | 46/41 |
| | | 199.212 |
| | | 41 |
| | |} |
| | |
| | ===Middle Major Seconds (200-220 cents)=== |
| | |
| | {| class="wikitable" |
| | |- |
| | ! ratio |
| | ! cents value |
| | ! prime limit |
| | |- |
| | | 9/8 = 27/24 = 45/40 |
| | | 203.910 |
| | | 3 |
| | |- |
| | | 44/39 |
| | | 208.835 |
| | | 13 |
| | |- |
| | | 35/31 |
| | | 210.104 |
| | | 31 |
| | |- |
| | | 26/23 |
| | | 212.253 |
| | | 23 |
| | |- |
| | | 43/38 |
| | | 214.005 |
| | | 43 |
| | |- |
| | | 17/15 |
| | | 216.687 |
| | | 17 |
| | |- |
| | | 42/37 |
| | | 219.437 |
| | | 37 |
| | |} |
| | |
| | ===Large Major Seconds (220-240 cents)=== |
| | |
| | {| class="wikitable" |
| | |- |
| | ! ratio |
| | ! cents value |
| | ! prime limit |
| | |- |
| | | 25/22 |
| | | 221.309 |
| | | 11 |
| | |- |
| | | 33/29 |
| | | 223.696 |
| | | 29 |
| | |- |
| | | 41/36 |
| | | 225.152 |
| | | 41 |
| | |- |
| | | 8/7 = 24/21 = 40/35 |
| | | 231.174 |
| | | 7 |
| | |- |
| | | 47/41 |
| | | 236.444 |
| | | 47 |
| | |- |
| | | 39/34 |
| | | 237.527 |
| | | 17 |
| | |- |
| | | 31/27 |
| | | 239.171 |
| | | 31 |
| | |} |
| | |
| | ==Interseptimal Region (M2-m3) (240-260 cents)== |
|
| |
|
| ==Minor Seconds (60-125 cents)== | | {| class="wikitable" |
| ===Small Minor Seconds (60-80 cents)===
| | |- |
| ||~ ratio ||~ cents value ||~ prime limit ||
| | ! ratio |
| || 29/28 || 60.751 || 29 || | | ! cents value |
| || 28/27 || 62.961 || 7 || | | ! prime limit |
| || 27/26 || 65.337 || 13 || | | |- |
| || 26/25 || 67.900 || 13 || | | | 54/47 |
| || 25/24 || 70.672 || 5 || | | | 240.358 |
| || 24/23 || 73.681 || 23 || | | | 47 |
| || 47/45 || 75.283 || 47 || | | |- |
| || 23/22 || 76.956 || 23 ||
| | | 23/20 |
| || 45/43 || 78.706 || 43 || | | | 241.961 |
| ===Middle Minor Seconds (80-100 cents)===
| | | 23 |
| ||~ ratio ||~ cents value ||~ prime limit || | | |- |
| || 22/21 || 80.537 || 11 || | | | 38/33 |
| || 43/41 || 82.455 || 43 || | | | 244.240 |
| || 21/20 || 84.467 || 7 || | | | 19 |
| || 41/39 || 86.580 || 41 ||
| | |- |
| || 20/19 || 88.801 || 19 || | | | 15/13 = 45/39 |
| || 39/37 || 91.139 || 37 || | | | 247.741 |
| || 19/18 || 93.603 || 19 || | | | 13 |
| || 37/35 || 96.204 || 37 ||
| | |- |
| || 18/17 || 98.955 || 17 || | | | 52/45 |
| ===Large Minor Seconds (100-125 cents)===
| | | 250.304 |
| ||~ ratio ||~ cents value ||~ prime limit || | | | 13 |
| || 35/33 || 101.867 || 11 ||
| | |- |
| || 17/16 || 104.955 || 17 || | | | 37/32 |
| || 50/47 || 107.121 || 47 || | | | 251.344 |
| || 33/31 || 108.237 || 31 || | | | 37 |
| || 16/15 = 48/45 || 111.731 || 5 || | | |- |
| || 47/44 || 114.189 || 47 || | | | 22/19 |
| || 31/29 || 115.458 || 31 || | | | 253.805 |
| || 46/43 || 116.757 || 43 || | | | 19 |
| || 15/14 = 45/42 || 119.443 || 7 || | | |- |
| || 44/41 || 122.256 || 41 || | | | 29/25 |
| || 29/27 || 123.712 || 29 || | | | 256.950 |
| | | 29 |
| | |- |
| | | 36/31 |
| | | 258.874 |
| | | 31 |
| | |} |
|
| |
|
| ==Central or Zalzalian Seconds (formerly Neutral Seconds) (125-170 cents)== | | ==Minor Thirds (260-330 cents)== |
| ===Small Central Seconds (125-170 cents)===
| |
| ||~ ratio ||~ cents value ||~ prime limit ||
| |
| || 43/40 || 125.204 || 43 ||
| |
| || 14/13 = 42/39 || 128.298 || 13 ||
| |
| || 41/38 || 131.549 || 41 ||
| |
| || 27/25 || 133.238 || 5 ||
| |
| || 40/37 || 134.970 || 37 ||
| |
| ===Middle Central Seconds (135-160 cents)===
| |
| ||~ ratio ||~ cents value ||~ prime limit ||
| |
| || 13/12 = 39/36 || 138.573 || 13 ||
| |
| || 38/35 || 142.373 || 19 ||
| |
| || 25/23 || 144.353 || 23 ||
| |
| || 37/34 || 146.389 || 37 ||
| |
| || 12/11 = 36/33 || 150.637 || 11 ||
| |
| || 47/43 || 153.989 || 47 ||
| |
| || 35/32 || 155.140 || 7 ||
| |
| || 23/21 || 157.493 || 23 ||
| |
| || 34/31 || 159.920 || 31 ||
| |
| ===Large Central Seconds (160-170 cents)===
| |
| ====Beginning of Equable Heptatonic Region (160-182 cents)====
| |
| ||~ ratio ||~ cents value ||~ prime limit ||
| |
| || 45/41 || 161.161 || 41 ||
| |
| || 11/10 = 33/30 || 165.004 || 11 ||
| |
| || 43/39 || 169.035 || 43 ||
| |
| ====End of Large Central Seconds Region, continuation of Equable Heptatonic Region====
| |
| ||~ ratio ||~ cents value ||~ prime limit ||
| |
| || 32/29 || 170.423 || 29 ||
| |
| || 21/19 || 173.268 || 19 ||
| |
| || 52/47 || 175.021 || 47 ||
| |
| || 31/28 || 176.210 || 31 ||
| |
| || 41/37 || 177.718 || 41 ||
| |
| ====End of Equable Heptatonic Region.====
| |
|
| |
|
| ==Major Seconds (180-240 cents)==
| | ===Small Minor Thirds (260-280 cents)=== |
| ===Small Major Seconds (180-200 cents)===
| |
| ||~ ratio ||~ cents value ||~ prime limit ||
| |
| || 10/9 = 30/27 = 50/45 || 182.404 || 5 ||
| |
| || 39/35 || 187.343 || 13 ||
| |
| || 29/26 || 189.050 || 29 ||
| |
| || 19/17 || 192.558 || 19 ||
| |
| || 47/42 || 194.726 || 47 ||
| |
| || 28/25 || 196.198 || 7 ||
| |
| || 37/33 || 198.071 || 37 ||
| |
| || 46/41 || 199.212 || 41 ||
| |
| ===Middle Major Seconds (200-220 cents)===
| |
| ||~ ratio ||~ cents value ||~ prime limit ||
| |
| || 9/8 = 27/24 = 45/40 || 203.910 || 3 ||
| |
| || 44/39 || 208.835 || 13 ||
| |
| || 35/31 || 210.104 || 31 ||
| |
| || 26/23 || 212.253 || 23 ||
| |
| || 43/38 || 214.005 || 43 ||
| |
| || 17/15 || 216.687 || 17 ||
| |
| || 42/37 || 219.437 || 37 ||
| |
| ===Large Major Seconds (220-240 cents)===
| |
| ||~ ratio ||~ cents value ||~ prime limit ||
| |
| || 25/22 || 221.309 || 11 ||
| |
| || 33/29 || 223.696 || 29 ||
| |
| || 41/36 || 225.152 || 41 ||
| |
| || 8/7 = 24/21 = 40/35 || 231.174 || 7 ||
| |
| || 47/41 || 236.444 || 47 ||
| |
| || 39/34 || 237.527 || 17 ||
| |
| || 31/27 || 239.171 || 31 ||
| |
| ==Interseptimal Region (M2-m3) (240-260 cents)==
| |
| ||~ ratio ||~ cents value ||~ prime limit ||
| |
| || 54/47 || 240.358 || 47 ||
| |
| || 23/20 || 241.961 || 23 ||
| |
| || 38/33 || 244.240 || 19 ||
| |
| || 15/13 = 45/39 || 247.741 || 13 ||
| |
| || 52/45 || 250.304 || 13 ||
| |
| || 37/32 || 251.344 || 37 ||
| |
| || 22/19 || 253.805 || 19 ||
| |
| || 29/25 || 256.950 || 29 ||
| |
| || 36/31 || 258.874 || 31 ||
| |
| == ==
| |
| ==Minor Thirds (260-330 cents)==
| |
| ===Small Minor Thirds (260-280 cents)=== | |
| ||~ ratio ||~ cents value ||~ prime limit ||
| |
| || 43/37 || 260.174 || 43 ||
| |
| || 50/43 || 261.110 || 43 ||
| |
| || 7/6 = 21/18 = 35/30 || 266.871 || 7 ||
| |
| || 48/41 || 272.893 || 41 ||
| |
| || 41/35 || 273.923 || 41 ||
| |
| || 34/29 || 275.378 || 29 ||
| |
| || 27/23 || 277.591 || 23 ||
| |
| || 47/40 || 279.193 || 47 ||
| |
| ===Middle Minor Thirds (280-300 cents)===
| |
| ||~ ratio ||~ cents value ||~ prime limit ||
| |
| || 20/17 || 281.358 || 17 ||
| |
| || 33/28 || 284.447 || 11 ||
| |
| || 46/39 || 285.792 || 23 ||
| |
| || 13/11 = 39/33 || 289.210 || 13 ||
| |
| || 45/38 || 292.711 || 19 ||
| |
| || 32/27 || 294.135 || 3 ||
| |
| || 19/16 || 297.513 || 19 ||
| |
| || 44/37 || 299.974 || 37 ||
| |
| ===Large Minor Thirds (300-330 cents)===
| |
| ||~ ratio ||~ cents value ||~ prime limit ||
| |
| || 25/21 || 301.847 || 7 ||
| |
| || 56/47 || 303.319 || 47 ||
| |
| || 31/26 || 304.508 || 31 ||
| |
| || 37/31 || 306.308 || 37 ||
| |
| || 43/36 || 307.608 || 43 ||
| |
| || 6/5 = 18/15 = 30/25 = 42/35 = 54/45 || 315.641 || 5 ||
| |
| || 47/39 || 323.024 || 47 ||
| |
| || 41/34 || 324.107 || 41 ||
| |
| || 35/29 || 325.562 || 29 ||
| |
| || 29/24 || 327.622 || 29 ||
| |
| || 52/43 || 329.010 || 43 ||
| |
| == ==
| |
| ==Central or Zalzalian Thirds (formerly Neutral Thirds) (330-372 cents)==
| |
| ===Small Central Thirds (330-342 cents)===
| |
| ||~ ratio ||~ cents value ||~ prime limit ||
| |
| || 23/19 || 330.761 || 23 ||
| |
| || 40/33 || 333.041 || 11 ||
| |
| || 17/14 || 336.130 || 17 ||
| |
| || 45/37 || 338.880 || 37 ||
| |
| || 28/23 || 340.552 || 23 ||
| |
| ===Middle Central Thirds (342-360 cents)===
| |
| ||~ ratio ||~ cents value ||~ prime limit ||
| |
| || 39/32 || 342.483 || 13 ||
| |
| || 50/41 || 343.565 || 41 ||
| |
| || 11/9 = 33/27 || 347.408 || 11 ||
| |
| || 38/31 || 352.477 || 31 ||
| |
| || 27/22 || 354.547 || 11 ||
| |
| || 43/35 || 356.378 || 43 ||
| |
| || 16/13 = 48/39 || 359.472 || 13 ||
| |
| ===Large Central Thirds (360-372 cents)===
| |
| ||~ ratio ||~ cents value ||~ prime limit ||
| |
| || 37/30 || 363.075 || 37 ||
| |
| || 58/47 || 364.071 || 47 ||
| |
| || 21/17 || 365.825 || 17 ||
| |
| || 47/38 || 367.994 || 47 ||
| |
| || 26/21 || 369.747 || 13 ||
| |
|
| |
|
| ==Major Thirds (372-440 cents)== | | {| class="wikitable" |
| ===Small Major Thirds (372-400 cents)===
| | |- |
| ||~ ratio ||~ cents value ||~ prime limit ||
| | ! ratio |
| || 31/25 || 372.408 || 31 || | | ! cents value |
| || 36/29 || 374.333 || 29 || | | ! prime limit |
| || 41/33 || 375.789 || 41 || | | |- |
| || 46/37 || 376.930 || 37 || | | | 43/37 |
| || 56/45 || 378.602 || 7 ||
| | | 260.174 |
| || 5/4 = 15/12 = 25/20 = 35/28 = 45/36 || 386.314 || 5 ||
| | | 43 |
| || 54/43 || 394.347 || 43 || | | |- |
| || 44/35 || 396.178 || 11 || | | | 50/43 |
| || 39/31 || 397.447 || 31 || | | | 261.110 |
| || 34/27 || 399.090 || 17 || | | | 43 |
| | |- |
| | | 7/6 = 21/18 = 35/30 |
| | | 266.871 |
| | | 7 |
| | |- |
| | | 48/41 |
| | | 272.893 |
| | | 41 |
| | |- |
| | | 41/35 |
| | | 273.923 |
| | | 41 |
| | |- |
| | | 34/29 |
| | | 275.378 |
| | | 29 |
| | |- |
| | | 27/23 |
| | | 277.591 |
| | | 23 |
| | |- |
| | | 47/40 |
| | | 279.193 |
| | | 47 |
| | |} |
|
| |
|
| ...to be continued...</pre></div>
| | ===Middle Minor Thirds (280-300 cents)=== |
| <h4>Original HTML content:</h4>
| |
| <div style="width:100%; max-height:400pt; overflow:auto; background-color:#f8f9fa; border: 1px solid #eaecf0; padding:0em"><pre style="margin:0px;border:none;background:none;word-wrap:break-word;width:200%;white-space: pre-wrap ! important" class="old-revision-html"><html><head><title>47-limit</title></head><body>The 47-limit. Whoa.<br />
| |
| <br />
| |
| Here is a list of the intervals within the octave belonging to the 47-odd limit -- that is, intervals between 1/1 and 2/1 which contain no odd numbers greater than 47. It is organized by <a class="wiki_link" href="/interval%20category">interval category</a> according to the Schulter System outlined in <a class="wiki_link_ext" href="http://www.bestii.com/~mschulter/IntervalSpectrumRegions.txt" rel="nofollow">Regions of the Interval Spectrum</a>.<br />
| |
| <br />
| |
| <!-- ws:start:WikiTextHeadingRule:0:&lt;h2&gt; --><h2 id="toc0"><a name="x-Pure Unison (0 cents)"></a><!-- ws:end:WikiTextHeadingRule:0 -->Pure Unison (0 cents)</h2>
| |
|
| |
|
| |
|
| <table class="wiki_table">
| | {| class="wikitable" |
| <tr>
| | |- |
| <th>ratio<br />
| | ! ratio |
| </th>
| | ! cents value |
| <th>cents value<br />
| | ! prime limit |
| </th>
| | |- |
| </tr>
| | | 20/17 |
| <tr>
| | | 281.358 |
| <td>1/1<br />
| | | 17 |
| </td>
| | |- |
| <td>0<br />
| | | 33/28 |
| </td>
| | | 284.447 |
| </tr>
| | | 11 |
| </table>
| | |- |
| | | 46/39 |
| | | 285.792 |
| | | 23 |
| | |- |
| | | 13/11 = 39/33 |
| | | 289.210 |
| | | 13 |
| | |- |
| | | 45/38 |
| | | 292.711 |
| | | 19 |
| | |- |
| | | 32/27 |
| | | 294.135 |
| | | 3 |
| | |- |
| | | 19/16 |
| | | 297.513 |
| | | 19 |
| | |- |
| | | 44/37 |
| | | 299.974 |
| | | 37 |
| | |} |
|
| |
|
| <br />
| | ===Large Minor Thirds (300-330 cents)=== |
| <!-- ws:start:WikiTextHeadingRule:2:&lt;h2&gt; --><h2 id="toc1"><a name="x-Commas (0-30 cents)"></a><!-- ws:end:WikiTextHeadingRule:2 -->Commas (0-30 cents)</h2>
| |
| None within the 47-odd limit.<br />
| |
| <br />
| |
| <!-- ws:start:WikiTextHeadingRule:4:&lt;h2&gt; --><h2 id="toc2"><a name="x-Dieses (30-60 cents)"></a><!-- ws:end:WikiTextHeadingRule:4 -->Dieses (30-60 cents)</h2>
| |
|
| |
|
| |
|
| <table class="wiki_table">
| | {| class="wikitable" |
| <tr>
| | |- |
| <th>ratio<br />
| | ! ratio |
| </th>
| | ! cents value |
| <th>cents value<br />
| | ! prime limit |
| </th>
| | |- |
| <th>prime limit<br />
| | | 25/21 |
| </th>
| | | 301.847 |
| </tr>
| | | 7 |
| <tr>
| | |- |
| <td>48/47<br />
| | | 56/47 |
| </td>
| | | 303.319 |
| <td>36.448<br />
| | | 47 |
| </td>
| | |- |
| <td>47<br />
| | | 31/26 |
| </td>
| | | 304.508 |
| </tr>
| | | 31 |
| <tr>
| | |- |
| <td>47/46<br />
| | | 37/31 |
| </td>
| | | 306.308 |
| <td>37.232<br />
| | | 37 |
| </td>
| | |- |
| <td>47<br />
| | | 43/36 |
| </td>
| | | 307.608 |
| </tr>
| | | 43 |
| <tr>
| | |- |
| <td>46/45<br />
| | | 6/5 = 18/15 = 30/25 = 42/35 = 54/45 |
| </td>
| | | 315.641 |
| <td>38.051<br />
| | | 5 |
| </td>
| | |- |
| <td>23<br />
| | | 47/39 |
| </td>
| | | 323.024 |
| </tr>
| | | 47 |
| <tr>
| | |- |
| <td>45/44<br />
| | | 41/34 |
| </td>
| | | 324.107 |
| <td>38.906<br />
| | | 41 |
| </td>
| | |- |
| <td>11<br />
| | | 35/29 |
| </td>
| | | 325.562 |
| </tr>
| | | 29 |
| <tr>
| | |- |
| <td>44/43<br />
| | | 29/24 |
| </td>
| | | 327.622 |
| <td>39.800<br />
| | | 29 |
| </td>
| | |- |
| <td>43<br />
| | | 52/43 |
| </td>
| | | 329.010 |
| </tr>
| | | 43 |
| <tr>
| | |} |
| <td>43/42<br />
| |
| </td>
| |
| <td>40.737<br />
| |
| </td>
| |
| <td>43<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>42/41<br />
| |
| </td>
| |
| <td>41.719<br />
| |
| </td>
| |
| <td>41<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>41/40<br />
| |
| </td>
| |
| <td>42.749<br />
| |
| </td>
| |
| <td>41<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>40/39<br />
| |
| </td>
| |
| <td>43.831<br />
| |
| </td>
| |
| <td>13<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>39/38<br />
| |
| </td>
| |
| <td>44.970<br />
| |
| </td>
| |
| <td>19<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>38/37<br />
| |
| </td>
| |
| <td>46/169<br />
| |
| </td>
| |
| <td>37<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>37/36<br />
| |
| </td>
| |
| <td>47.434<br />
| |
| </td>
| |
| <td>37<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>36/35<br />
| |
| </td>
| |
| <td>48.770<br />
| |
| </td>
| |
| <td>7<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>35/34<br />
| |
| </td>
| |
| <td>50.184<br />
| |
| </td>
| |
| <td>17<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>34/33<br />
| |
| </td>
| |
| <td>51.682<br />
| |
| </td>
| |
| <td>17<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>33/32<br />
| |
| </td>
| |
| <td>53.273<br />
| |
| </td>
| |
| <td>11<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>32/31<br />
| |
| </td>
| |
| <td>54.964<br />
| |
| </td>
| |
| <td>31<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>31/30<br />
| |
| </td>
| |
| <td>56.767<br />
| |
| </td>
| |
| <td>31<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>30/29<br />
| |
| </td>
| |
| <td>58.692<br />
| |
| </td>
| |
| <td>29<br />
| |
| </td>
| |
| </tr>
| |
| </table>
| |
|
| |
|
| <br />
| | ==Central or Zalzalian Thirds (formerly Neutral Thirds) (330-372 cents)== |
| <!-- ws:start:WikiTextHeadingRule:6:&lt;h2&gt; --><h2 id="toc3"><a name="x-Minor Seconds (60-125 cents)"></a><!-- ws:end:WikiTextHeadingRule:6 -->Minor Seconds (60-125 cents)</h2>
| |
| <!-- ws:start:WikiTextHeadingRule:8:&lt;h3&gt; --><h3 id="toc4"><a name="x-Minor Seconds (60-125 cents)-Small Minor Seconds (60-80 cents)"></a><!-- ws:end:WikiTextHeadingRule:8 -->Small Minor Seconds (60-80 cents)</h3>
| |
|
| |
|
| |
|
| <table class="wiki_table">
| | ===Small Central Thirds (330-342 cents)=== |
| <tr>
| |
| <th>ratio<br />
| |
| </th>
| |
| <th>cents value<br />
| |
| </th>
| |
| <th>prime limit<br />
| |
| </th>
| |
| </tr>
| |
| <tr>
| |
| <td>29/28<br />
| |
| </td>
| |
| <td>60.751<br />
| |
| </td>
| |
| <td>29<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>28/27<br />
| |
| </td>
| |
| <td>62.961<br />
| |
| </td>
| |
| <td>7<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>27/26<br />
| |
| </td>
| |
| <td>65.337<br />
| |
| </td>
| |
| <td>13<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>26/25<br />
| |
| </td>
| |
| <td>67.900<br />
| |
| </td>
| |
| <td>13<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>25/24<br />
| |
| </td>
| |
| <td>70.672<br />
| |
| </td>
| |
| <td>5<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>24/23<br />
| |
| </td>
| |
| <td>73.681<br />
| |
| </td>
| |
| <td>23<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>47/45<br />
| |
| </td>
| |
| <td>75.283<br />
| |
| </td>
| |
| <td>47<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>23/22<br />
| |
| </td>
| |
| <td>76.956<br />
| |
| </td>
| |
| <td>23<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>45/43<br />
| |
| </td>
| |
| <td>78.706<br />
| |
| </td>
| |
| <td>43<br />
| |
| </td>
| |
| </tr>
| |
| </table>
| |
|
| |
|
| <!-- ws:start:WikiTextHeadingRule:10:&lt;h3&gt; --><h3 id="toc5"><a name="x-Minor Seconds (60-125 cents)-Middle Minor Seconds (80-100 cents)"></a><!-- ws:end:WikiTextHeadingRule:10 -->Middle Minor Seconds (80-100 cents)</h3>
| | {| class="wikitable" |
|
| | |- |
| | ! ratio |
| | ! cents value |
| | ! prime limit |
| | |- |
| | | 23/19 |
| | | 330.761 |
| | | 23 |
| | |- |
| | | 40/33 |
| | | 333.041 |
| | | 11 |
| | |- |
| | | 17/14 |
| | | 336.130 |
| | | 17 |
| | |- |
| | | 45/37 |
| | | 338.880 |
| | | 37 |
| | |- |
| | | 28/23 |
| | | 340.552 |
| | | 23 |
| | |} |
|
| |
|
| <table class="wiki_table">
| | ===Middle Central Thirds (342-360 cents)=== |
| <tr>
| |
| <th>ratio<br />
| |
| </th>
| |
| <th>cents value<br />
| |
| </th>
| |
| <th>prime limit<br />
| |
| </th>
| |
| </tr>
| |
| <tr>
| |
| <td>22/21<br />
| |
| </td>
| |
| <td>80.537<br />
| |
| </td>
| |
| <td>11<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>43/41<br />
| |
| </td>
| |
| <td>82.455<br />
| |
| </td>
| |
| <td>43<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>21/20<br />
| |
| </td>
| |
| <td>84.467<br />
| |
| </td>
| |
| <td>7<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>41/39<br />
| |
| </td>
| |
| <td>86.580<br />
| |
| </td>
| |
| <td>41<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>20/19<br />
| |
| </td>
| |
| <td>88.801<br />
| |
| </td>
| |
| <td>19<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>39/37<br />
| |
| </td>
| |
| <td>91.139<br />
| |
| </td>
| |
| <td>37<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>19/18<br />
| |
| </td>
| |
| <td>93.603<br />
| |
| </td>
| |
| <td>19<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>37/35<br />
| |
| </td>
| |
| <td>96.204<br />
| |
| </td>
| |
| <td>37<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>18/17<br />
| |
| </td>
| |
| <td>98.955<br />
| |
| </td>
| |
| <td>17<br />
| |
| </td>
| |
| </tr>
| |
| </table>
| |
|
| |
|
| <!-- ws:start:WikiTextHeadingRule:12:&lt;h3&gt; --><h3 id="toc6"><a name="x-Minor Seconds (60-125 cents)-Large Minor Seconds (100-125 cents)"></a><!-- ws:end:WikiTextHeadingRule:12 -->Large Minor Seconds (100-125 cents)</h3>
| | {| class="wikitable" |
|
| | |- |
| | ! ratio |
| | ! cents value |
| | ! prime limit |
| | |- |
| | | 39/32 |
| | | 342.483 |
| | | 13 |
| | |- |
| | | 50/41 |
| | | 343.565 |
| | | 41 |
| | |- |
| | | 11/9 = 33/27 |
| | | 347.408 |
| | | 11 |
| | |- |
| | | 38/31 |
| | | 352.477 |
| | | 31 |
| | |- |
| | | 27/22 |
| | | 354.547 |
| | | 11 |
| | |- |
| | | 43/35 |
| | | 356.378 |
| | | 43 |
| | |- |
| | | 16/13 = 48/39 |
| | | 359.472 |
| | | 13 |
| | |} |
|
| |
|
| <table class="wiki_table">
| | ===Large Central Thirds (360-372 cents)=== |
| <tr>
| |
| <th>ratio<br />
| |
| </th>
| |
| <th>cents value<br />
| |
| </th>
| |
| <th>prime limit<br />
| |
| </th>
| |
| </tr>
| |
| <tr>
| |
| <td>35/33<br />
| |
| </td>
| |
| <td>101.867<br />
| |
| </td>
| |
| <td>11<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>17/16<br />
| |
| </td>
| |
| <td>104.955<br />
| |
| </td>
| |
| <td>17<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>50/47<br />
| |
| </td>
| |
| <td>107.121<br />
| |
| </td>
| |
| <td>47<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>33/31<br />
| |
| </td>
| |
| <td>108.237<br />
| |
| </td>
| |
| <td>31<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>16/15 = 48/45<br />
| |
| </td>
| |
| <td>111.731<br />
| |
| </td>
| |
| <td>5<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>47/44<br />
| |
| </td>
| |
| <td>114.189<br />
| |
| </td>
| |
| <td>47<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>31/29<br />
| |
| </td>
| |
| <td>115.458<br />
| |
| </td>
| |
| <td>31<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>46/43<br />
| |
| </td>
| |
| <td>116.757<br />
| |
| </td>
| |
| <td>43<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>15/14 = 45/42<br />
| |
| </td>
| |
| <td>119.443<br />
| |
| </td>
| |
| <td>7<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>44/41<br />
| |
| </td>
| |
| <td>122.256<br />
| |
| </td>
| |
| <td>41<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>29/27<br />
| |
| </td>
| |
| <td>123.712<br />
| |
| </td>
| |
| <td>29<br />
| |
| </td>
| |
| </tr>
| |
| </table>
| |
|
| |
|
| <br />
| | {| class="wikitable" |
| <!-- ws:start:WikiTextHeadingRule:14:&lt;h2&gt; --><h2 id="toc7"><a name="x-Central or Zalzalian Seconds (formerly Neutral Seconds) (125-170 cents)"></a><!-- ws:end:WikiTextHeadingRule:14 -->Central or Zalzalian Seconds (formerly Neutral Seconds) (125-170 cents)</h2>
| | |- |
| <!-- ws:start:WikiTextHeadingRule:16:&lt;h3&gt; --><h3 id="toc8"><a name="x-Central or Zalzalian Seconds (formerly Neutral Seconds) (125-170 cents)-Small Central Seconds (125-170 cents)"></a><!-- ws:end:WikiTextHeadingRule:16 -->Small Central Seconds (125-170 cents)</h3>
| | ! ratio |
|
| | ! cents value |
| | ! prime limit |
| | |- |
| | | 37/30 |
| | | 363.075 |
| | | 37 |
| | |- |
| | | 58/47 |
| | | 364.071 |
| | | 47 |
| | |- |
| | | 21/17 |
| | | 365.825 |
| | | 17 |
| | |- |
| | | 47/38 |
| | | 367.994 |
| | | 47 |
| | |- |
| | | 26/21 |
| | | 369.747 |
| | | 13 |
| | |} |
|
| |
|
| <table class="wiki_table">
| | ==Major Thirds (372-440 cents)== |
| <tr>
| |
| <th>ratio<br />
| |
| </th>
| |
| <th>cents value<br />
| |
| </th>
| |
| <th>prime limit<br />
| |
| </th>
| |
| </tr>
| |
| <tr>
| |
| <td>43/40<br />
| |
| </td>
| |
| <td>125.204<br />
| |
| </td>
| |
| <td>43<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>14/13 = 42/39<br />
| |
| </td>
| |
| <td>128.298<br />
| |
| </td>
| |
| <td>13<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>41/38<br />
| |
| </td>
| |
| <td>131.549<br />
| |
| </td>
| |
| <td>41<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>27/25<br />
| |
| </td>
| |
| <td>133.238<br />
| |
| </td>
| |
| <td>5<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>40/37<br />
| |
| </td>
| |
| <td>134.970<br />
| |
| </td>
| |
| <td>37<br />
| |
| </td>
| |
| </tr>
| |
| </table>
| |
|
| |
|
| <!-- ws:start:WikiTextHeadingRule:18:&lt;h3&gt; --><h3 id="toc9"><a name="x-Central or Zalzalian Seconds (formerly Neutral Seconds) (125-170 cents)-Middle Central Seconds (135-160 cents)"></a><!-- ws:end:WikiTextHeadingRule:18 -->Middle Central Seconds (135-160 cents)</h3>
| | ===Small Major Thirds (372-400 cents)=== |
|
| |
|
| |
|
| <table class="wiki_table">
| | {| class="wikitable" |
| <tr>
| | |- |
| <th>ratio<br />
| | ! ratio |
| </th>
| | ! cents value |
| <th>cents value<br />
| | ! prime limit |
| </th>
| | |- |
| <th>prime limit<br />
| | | 31/25 |
| </th>
| | | 372.408 |
| </tr>
| | | 31 |
| <tr>
| | |- |
| <td>13/12 = 39/36<br />
| | | 36/29 |
| </td>
| | | 374.333 |
| <td>138.573<br />
| | | 29 |
| </td>
| | |- |
| <td>13<br />
| | | 41/33 |
| </td>
| | | 375.789 |
| </tr>
| | | 41 |
| <tr>
| | |- |
| <td>38/35<br />
| | | 46/37 |
| </td>
| | | 376.930 |
| <td>142.373<br />
| | | 37 |
| </td>
| | |- |
| <td>19<br />
| | | 56/45 |
| </td>
| | | 378.602 |
| </tr>
| | | 7 |
| <tr>
| | |- |
| <td>25/23<br />
| | | 5/4 = 15/12 = 25/20 = 35/28 = 45/36 |
| </td>
| | | 386.314 |
| <td>144.353<br />
| | | 5 |
| </td>
| | |- |
| <td>23<br />
| | | 54/43 |
| </td>
| | | 394.347 |
| </tr>
| | | 43 |
| <tr>
| | |- |
| <td>37/34<br />
| | | 44/35 |
| </td>
| | | 396.178 |
| <td>146.389<br />
| | | 11 |
| </td>
| | |- |
| <td>37<br />
| | | 39/31 |
| </td>
| | | 397.447 |
| </tr>
| | | 31 |
| <tr>
| | |- |
| <td>12/11 = 36/33<br />
| | | 34/27 |
| </td>
| | | 399.090 |
| <td>150.637<br />
| | | 17 |
| </td>
| | |} |
| <td>11<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>47/43<br />
| |
| </td>
| |
| <td>153.989<br />
| |
| </td>
| |
| <td>47<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>35/32<br />
| |
| </td>
| |
| <td>155.140<br />
| |
| </td>
| |
| <td>7<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>23/21<br />
| |
| </td>
| |
| <td>157.493<br />
| |
| </td>
| |
| <td>23<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>34/31<br />
| |
| </td>
| |
| <td>159.920<br />
| |
| </td>
| |
| <td>31<br />
| |
| </td>
| |
| </tr>
| |
| </table>
| |
|
| |
|
| <!-- ws:start:WikiTextHeadingRule:20:&lt;h3&gt; --><h3 id="toc10"><a name="x-Central or Zalzalian Seconds (formerly Neutral Seconds) (125-170 cents)-Large Central Seconds (160-170 cents)"></a><!-- ws:end:WikiTextHeadingRule:20 -->Large Central Seconds (160-170 cents)</h3>
| | ===Middle Major Thirds (400-423 cents)=== |
| <!-- ws:start:WikiTextHeadingRule:22:&lt;h4&gt; --><h4 id="toc11"><a name="x-Central or Zalzalian Seconds (formerly Neutral Seconds) (125-170 cents)-Large Central Seconds (160-170 cents)-Beginning of Equable Heptatonic Region (160-182 cents)"></a><!-- ws:end:WikiTextHeadingRule:22 -->Beginning of Equable Heptatonic Region (160-182 cents)</h4>
| |
|
| |
|
| |
|
| <table class="wiki_table">
| | {| class="wikitable" |
| <tr>
| | |- |
| <th>ratio<br />
| | ! ratio |
| </th>
| | ! cents value |
| <th>cents value<br />
| | ! prime limit |
| </th>
| | |- |
| <th>prime limit<br />
| | | 29/23 |
| </th>
| | | 401.303 |
| </tr>
| | | 29 |
| <tr>
| | |- |
| <td>45/41<br />
| | | [[24/19]] |
| </td>
| | | 404.442 |
| <td>161.161<br />
| | | 19 |
| </td>
| | |- |
| <td>41<br />
| | | 43/34 |
| </td>
| | | 406.562 |
| </tr>
| | | 43 |
| <tr>
| | |- |
| <td>11/10 = 33/30<br />
| | | [[19/15]] |
| </td>
| | | 409.244 |
| <td>165.004<br />
| | | 19 |
| </td>
| | |- |
| <td>11<br />
| | | 52/41 |
| </td>
| | | 411.465 |
| </tr>
| | | 41 |
| <tr>
| | |- |
| <td>43/39<br />
| | | [[33/26]] |
| </td>
| | | 412.745 |
| <td>169.035<br />
| | | 13 |
| </td>
| | |- |
| <td>43<br />
| | | [[47/37]] |
| </td>
| | | 414.163 |
| </tr>
| | | 47 |
| </table>
| | |- |
| | | [[14/11]] = 42/33 |
| | | 417.508 |
| | | 11 |
| | |- |
| | | [[37/29]] |
| | | 421.767 |
| | | 37 |
| | |- |
| | | 60/47 |
| | | 422.762 |
| | | 47 |
| | |} |
|
| |
|
| <!-- ws:start:WikiTextHeadingRule:24:&lt;h4&gt; --><h4 id="toc12"><a name="x-Central or Zalzalian Seconds (formerly Neutral Seconds) (125-170 cents)-Large Central Seconds (160-170 cents)-End of Large Central Seconds Region, continuation of Equable Heptatonic Region"></a><!-- ws:end:WikiTextHeadingRule:24 -->End of Large Central Seconds Region, continuation of Equable Heptatonic Region</h4>
| | ===Large Major Thirds (423-440 cents)=== |
|
| |
|
| |
|
| <table class="wiki_table">
| | {| class="wikitable" |
| <tr>
| | |- |
| <th>ratio<br />
| | ! ratio |
| </th>
| | ! cents value |
| <th>cents value<br />
| | ! prime limit |
| </th>
| | |- |
| <th>prime limit<br />
| | | 23/18 |
| </th>
| | | 424.364 |
| </tr>
| | | 23 |
| <tr>
| | |- |
| <td>32/29<br />
| | | 32/25 |
| </td>
| | | 427.373 |
| <td>170.423<br />
| | | 5 |
| </td>
| | |- |
| <td>29<br />
| | | 41/32 |
| </td>
| | | 429.062 |
| </tr>
| | | 41 |
| <tr>
| | |- |
| <td>21/19<br />
| | | 50/39 |
| </td>
| | | 430.145 |
| <td>173.268<br />
| | | 13 |
| </td>
| | |- |
| <td>19<br />
| | | 9/7 = 27/21 = 45/35 |
| </td>
| | | 435.084 |
| </tr>
| | | 7 |
| <tr>
| | |- |
| <td>52/47<br />
| | | 58/45 |
| </td>
| | | 439.353 |
| <td>175.021<br />
| | | 29 |
| </td>
| | |} |
| <td>47<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>31/28<br />
| |
| </td>
| |
| <td>176.210<br />
| |
| </td>
| |
| <td>31<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>41/37<br />
| |
| </td>
| |
| <td>177.718<br />
| |
| </td>
| |
| <td>41<br />
| |
| </td>
| |
| </tr>
| |
| </table>
| |
|
| |
|
| <!-- ws:start:WikiTextHeadingRule:26:&lt;h4&gt; --><h4 id="toc13"><a name="x-Central or Zalzalian Seconds (formerly Neutral Seconds) (125-170 cents)-Large Central Seconds (160-170 cents)-End of Equable Heptatonic Region."></a><!-- ws:end:WikiTextHeadingRule:26 -->End of Equable Heptatonic Region.</h4>
| | ==Interseptimal Region (M3-4) (440-468 cents)== |
| <br />
| |
| <!-- ws:start:WikiTextHeadingRule:28:&lt;h2&gt; --><h2 id="toc14"><a name="x-Major Seconds (180-240 cents)"></a><!-- ws:end:WikiTextHeadingRule:28 -->Major Seconds (180-240 cents)</h2>
| |
| <!-- ws:start:WikiTextHeadingRule:30:&lt;h3&gt; --><h3 id="toc15"><a name="x-Major Seconds (180-240 cents)-Small Major Seconds (180-200 cents)"></a><!-- ws:end:WikiTextHeadingRule:30 -->Small Major Seconds (180-200 cents)</h3>
| |
|
| |
|
| |
|
| <table class="wiki_table">
| | {| class="wikitable" |
| <tr>
| | |- |
| <th>ratio<br />
| | ! ratio |
| </th>
| | ! cents value |
| <th>cents value<br />
| | ! prime limit |
| </th>
| | |- |
| <th>prime limit<br />
| | | 40/31 |
| </th>
| | | 441.278 |
| </tr>
| | | 31 |
| <tr>
| | |- |
| <td>10/9 = 30/27 = 50/45<br />
| | | 31/24 |
| </td>
| | | 443.081 |
| <td>182.404<br />
| | | 31 |
| </td>
| | |- |
| <td>5<br />
| | | 22/17 |
| </td>
| | | 446.363 |
| </tr>
| | | 17 |
| <tr>
| | |- |
| <td>39/35<br />
| | | 35/27 |
| </td>
| | | 449.275 |
| <td>187.343<br />
| | | 7 |
| </td>
| | |- |
| <td>13<br />
| | | 48/37 |
| </td>
| | | 450.611 |
| </tr>
| | | 37 |
| <tr>
| | |- |
| <td>29/26<br />
| | | 13/10 = 39/30 |
| </td>
| | | 454.214 |
| <td>189.050<br />
| | | 13 |
| </td>
| | |- |
| <td>29<br />
| | | 56/43 |
| </td>
| | | 457.308 |
| </tr>
| | | 43 |
| <tr>
| | |- |
| <td>19/17<br />
| | | 43/33 |
| </td>
| | | 458.245 |
| <td>192.558<br />
| | | 43 |
| </td>
| | |- |
| <td>19<br />
| | | 30/23 |
| </td>
| | | 459.994 |
| </tr>
| | | 23 |
| <tr>
| | |- |
| <td>47/42<br />
| | | 47/36 |
| </td>
| | | 461.597 |
| <td>194.726<br />
| | | 47 |
| </td>
| | |- |
| <td>47<br />
| | | 17/13 |
| </td>
| | | 464.428 |
| </tr>
| | | 17 |
| <tr>
| | |- |
| <td>28/25<br />
| | | 38/29 |
| </td>
| | | 467.936 |
| <td>196.198<br />
| | | 29 |
| </td>
| | |} |
| <td>7<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>37/33<br />
| |
| </td>
| |
| <td>198.071<br />
| |
| </td>
| |
| <td>37<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>46/41<br />
| |
| </td>
| |
| <td>199.212<br />
| |
| </td>
| |
| <td>41<br />
| |
| </td>
| |
| </tr>
| |
| </table>
| |
|
| |
|
| <!-- ws:start:WikiTextHeadingRule:32:&lt;h3&gt; --><h3 id="toc16"><a name="x-Major Seconds (180-240 cents)-Middle Major Seconds (200-220 cents)"></a><!-- ws:end:WikiTextHeadingRule:32 -->Middle Major Seconds (200-220 cents)</h3>
| | ==Perfect Fourths (468-528 cents)== |
|
| |
|
| |
|
| <table class="wiki_table">
| | ===Small Perfect Fourths (468-491 cents)=== |
| <tr>
| |
| <th>ratio<br />
| |
| </th>
| |
| <th>cents value<br />
| |
| </th>
| |
| <th>prime limit<br />
| |
| </th>
| |
| </tr>
| |
| <tr>
| |
| <td>9/8 = 27/24 = 45/40<br />
| |
| </td>
| |
| <td>203.910<br />
| |
| </td>
| |
| <td>3<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>44/39<br />
| |
| </td>
| |
| <td>208.835<br />
| |
| </td>
| |
| <td>13<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>35/31<br />
| |
| </td>
| |
| <td>210.104<br />
| |
| </td>
| |
| <td>31<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>26/23<br />
| |
| </td>
| |
| <td>212.253<br />
| |
| </td>
| |
| <td>23<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>43/38<br />
| |
| </td>
| |
| <td>214.005<br />
| |
| </td>
| |
| <td>43<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>17/15<br />
| |
| </td>
| |
| <td>216.687<br />
| |
| </td>
| |
| <td>17<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>42/37<br />
| |
| </td>
| |
| <td>219.437<br />
| |
| </td>
| |
| <td>37<br />
| |
| </td>
| |
| </tr>
| |
| </table>
| |
|
| |
|
| <!-- ws:start:WikiTextHeadingRule:34:&lt;h3&gt; --><h3 id="toc17"><a name="x-Major Seconds (180-240 cents)-Large Major Seconds (220-240 cents)"></a><!-- ws:end:WikiTextHeadingRule:34 -->Large Major Seconds (220-240 cents)</h3>
| | {| class="wikitable" |
|
| | |- |
| | ! ratio |
| | ! cents value |
| | ! prime limit |
| | |- |
| | | 21/16 |
| | | 470.781 |
| | | 7 |
| | |- |
| | | 46/35 |
| | | 473.135 |
| | | 23 |
| | |- |
| | | 25/19 |
| | | 475.114 |
| | | 19 |
| | |- |
| | | 54/41 |
| | | 476.803 |
| | | 41 |
| | |- |
| | | 29/22 |
| | | 478.259 |
| | | 29 |
| | |- |
| | | 62/47 |
| | | 479.529 |
| | | 47 |
| | |- |
| | | 33/25 |
| | | 480.646 |
| | | 11 |
| | |- |
| | | 37/28 |
| | | 482.518 |
| | | 37 |
| | |- |
| | | 41/31 |
| | | 484.027 |
| | | 41 |
| | |- |
| | | 45/34 |
| | | 485.268 |
| | | 17 |
| | |} |
|
| |
|
| <table class="wiki_table">
| | ===Middle Perfect Fourths (491-505 cents)=== |
| <tr>
| |
| <th>ratio<br />
| |
| </th>
| |
| <th>cents value<br />
| |
| </th>
| |
| <th>prime limit<br />
| |
| </th>
| |
| </tr>
| |
| <tr>
| |
| <td>25/22<br />
| |
| </td>
| |
| <td>221.309<br />
| |
| </td>
| |
| <td>11<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>33/29<br />
| |
| </td>
| |
| <td>223.696<br />
| |
| </td>
| |
| <td>29<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>41/36<br />
| |
| </td>
| |
| <td>225.152<br />
| |
| </td>
| |
| <td>41<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>8/7 = 24/21 = 40/35<br />
| |
| </td>
| |
| <td>231.174<br />
| |
| </td>
| |
| <td>7<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>47/41<br />
| |
| </td>
| |
| <td>236.444<br />
| |
| </td>
| |
| <td>47<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>39/34<br />
| |
| </td>
| |
| <td>237.527<br />
| |
| </td>
| |
| <td>17<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>31/27<br />
| |
| </td>
| |
| <td>239.171<br />
| |
| </td>
| |
| <td>31<br />
| |
| </td>
| |
| </tr>
| |
| </table>
| |
|
| |
|
| <!-- ws:start:WikiTextHeadingRule:36:&lt;h2&gt; --><h2 id="toc18"><a name="x-Interseptimal Region (M2-m3) (240-260 cents)"></a><!-- ws:end:WikiTextHeadingRule:36 -->Interseptimal Region (M2-m3) (240-260 cents)</h2>
| | {| class="wikitable" |
|
| | |- |
| | ! ratio |
| | ! cents value |
| | ! prime limit |
| | |- |
| | | 4/3 = 12/9 = 20/15 = 36/27 = 36/27 = 44/33 = 52/39 = 60/45 |
| | | 498.045 |
| | | 3 |
| | |} |
|
| |
|
| <table class="wiki_table">
| | ===Large Perfect Fourths (505-528 cents)=== |
| <tr>
| |
| <th>ratio<br />
| |
| </th>
| |
| <th>cents value<br />
| |
| </th>
| |
| <th>prime limit<br />
| |
| </th>
| |
| </tr>
| |
| <tr>
| |
| <td>54/47<br />
| |
| </td>
| |
| <td>240.358<br />
| |
| </td>
| |
| <td>47<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>23/20<br />
| |
| </td>
| |
| <td>241.961<br />
| |
| </td>
| |
| <td>23<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>38/33<br />
| |
| </td>
| |
| <td>244.240<br />
| |
| </td>
| |
| <td>19<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>15/13 = 45/39<br />
| |
| </td>
| |
| <td>247.741<br />
| |
| </td>
| |
| <td>13<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>52/45<br />
| |
| </td>
| |
| <td>250.304<br />
| |
| </td>
| |
| <td>13<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>37/32<br />
| |
| </td>
| |
| <td>251.344<br />
| |
| </td>
| |
| <td>37<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>22/19<br />
| |
| </td>
| |
| <td>253.805<br />
| |
| </td>
| |
| <td>19<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>29/25<br />
| |
| </td>
| |
| <td>256.950<br />
| |
| </td>
| |
| <td>29<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>36/31<br />
| |
| </td>
| |
| <td>258.874<br />
| |
| </td>
| |
| <td>31<br />
| |
| </td>
| |
| </tr>
| |
| </table>
| |
|
| |
|
| <!-- ws:start:WikiTextHeadingRule:38:&lt;h2&gt; --><h2 id="toc19"><!-- ws:end:WikiTextHeadingRule:38 --> </h2>
| | {| class="wikitable" |
| <!-- ws:start:WikiTextHeadingRule:40:&lt;h2&gt; --><h2 id="toc20"><a name="x-Minor Thirds (260-330 cents)"></a><!-- ws:end:WikiTextHeadingRule:40 -->Minor Thirds (260-330 cents)</h2>
| | |- |
| <!-- ws:start:WikiTextHeadingRule:42:&lt;h3&gt; --><h3 id="toc21"><a name="x-Minor Thirds (260-330 cents)-Small Minor Thirds (260-280 cents)"></a><!-- ws:end:WikiTextHeadingRule:42 -->Small Minor Thirds (260-280 cents)</h3>
| | ! ratio |
|
| | ! cents value |
| | ! prime limit |
| | |- |
| | | 47/35 |
| | | 510.367 |
| | | 47 |
| | |- |
| | | 43/32 |
| | | 511.518 |
| | | 43 |
| | |- |
| | | 39/29 |
| | | 512.905 |
| | | 29 |
| | |- |
| | | 35/26 |
| | | 514.612 |
| | | 13 |
| | |- |
| | | 31/23 |
| | | 516.761 |
| | | 31 |
| | |- |
| | | 58/43 |
| | | 518.059 |
| | | 43 |
| | |- |
| | | 27/20 |
| | | 519.551 |
| | | 5 |
| | |- |
| | | 50/37 |
| | | 521.283 |
| | | 37 |
| | |- |
| | | 23/17 |
| | | 523.319 |
| | | 23 |
| | |- |
| | | 42/31 |
| | | 525.745 |
| | | 31 |
| | |} |
|
| |
|
| <table class="wiki_table">
| | ==Superfourths (528-560 cents)== |
| <tr>
| |
| <th>ratio<br />
| |
| </th>
| |
| <th>cents value<br />
| |
| </th>
| |
| <th>prime limit<br />
| |
| </th>
| |
| </tr>
| |
| <tr>
| |
| <td>43/37<br />
| |
| </td>
| |
| <td>260.174<br />
| |
| </td>
| |
| <td>43<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>50/43<br />
| |
| </td>
| |
| <td>261.110<br />
| |
| </td>
| |
| <td>43<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>7/6 = 21/18 = 35/30<br />
| |
| </td>
| |
| <td>266.871<br />
| |
| </td>
| |
| <td>7<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>48/41<br />
| |
| </td>
| |
| <td>272.893<br />
| |
| </td>
| |
| <td>41<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>41/35<br />
| |
| </td>
| |
| <td>273.923<br />
| |
| </td>
| |
| <td>41<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>34/29<br />
| |
| </td>
| |
| <td>275.378<br />
| |
| </td>
| |
| <td>29<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>27/23<br />
| |
| </td>
| |
| <td>277.591<br />
| |
| </td>
| |
| <td>23<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>47/40<br />
| |
| </td>
| |
| <td>279.193<br />
| |
| </td>
| |
| <td>47<br />
| |
| </td>
| |
| </tr>
| |
| </table>
| |
|
| |
|
| <!-- ws:start:WikiTextHeadingRule:44:&lt;h3&gt; --><h3 id="toc22"><a name="x-Minor Thirds (260-330 cents)-Middle Minor Thirds (280-300 cents)"></a><!-- ws:end:WikiTextHeadingRule:44 -->Middle Minor Thirds (280-300 cents)</h3>
| | {| class="wikitable" |
|
| | |- |
| | ! ratio |
| | ! cents value |
| | ! prime limit |
| | |- |
| | | 19/14 |
| | | 528.687 |
| | | 19 |
| | |- |
| | | 34/25 |
| | | 532.328 |
| | | 17 |
| | |- |
| | | 64/47 |
| | | 534.493 |
| | | 47 |
| | |- |
| | | 15/11 = 45/33 |
| | | 536.951 |
| | | 11 |
| | |- |
| | | 56/41 |
| | | 539.764 |
| | | 41 |
| | |- |
| | | 41/30 |
| | | 540.794 |
| | | 41 |
| | |- |
| | | 26/19 |
| | | 543.015 |
| | | 19 |
| | |- |
| | | 37/27 |
| | | 545.479 |
| | | 37 |
| | |- |
| | | 48/35 |
| | | 546.815 |
| | | 7 |
| | |- |
| | | 11/8 = 33/24 |
| | | 551.318 |
| | | 11 |
| | |- |
| | | 62/45 |
| | | 554.812 |
| | | 31 |
| | |- |
| | | 40/29 |
| | | 556.737 |
| | | 29 |
| | |- |
| | | 29/21 |
| | | 558.796 |
| | | 29 |
| | |- |
| | | 47/34 |
| | | 560.551 |
| | | 47 |
| | |} |
|
| |
|
| <table class="wiki_table">
| | ==Tritonic Region (560-640 cents)== |
| <tr>
| |
| <th>ratio<br />
| |
| </th>
| |
| <th>cents value<br />
| |
| </th>
| |
| <th>prime limit<br />
| |
| </th>
| |
| </tr>
| |
| <tr>
| |
| <td>20/17<br />
| |
| </td>
| |
| <td>281.358<br />
| |
| </td>
| |
| <td>17<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>33/28<br />
| |
| </td>
| |
| <td>284.447<br />
| |
| </td>
| |
| <td>11<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>46/39<br />
| |
| </td>
| |
| <td>285.792<br />
| |
| </td>
| |
| <td>23<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>13/11 = 39/33<br />
| |
| </td>
| |
| <td>289.210<br />
| |
| </td>
| |
| <td>13<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>45/38<br />
| |
| </td>
| |
| <td>292.711<br />
| |
| </td>
| |
| <td>19<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>32/27<br />
| |
| </td>
| |
| <td>294.135<br />
| |
| </td>
| |
| <td>3<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>19/16<br />
| |
| </td>
| |
| <td>297.513<br />
| |
| </td>
| |
| <td>19<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>44/37<br />
| |
| </td>
| |
| <td>299.974<br />
| |
| </td>
| |
| <td>37<br />
| |
| </td>
| |
| </tr>
| |
| </table>
| |
|
| |
|
| <!-- ws:start:WikiTextHeadingRule:46:&lt;h3&gt; --><h3 id="toc23"><a name="x-Minor Thirds (260-330 cents)-Large Minor Thirds (300-330 cents)"></a><!-- ws:end:WikiTextHeadingRule:46 -->Large Minor Thirds (300-330 cents)</h3>
| | ===Small Tritones (560-577 cents)=== |
|
| |
|
| |
|
| <table class="wiki_table">
| | {| class="wikitable" |
| <tr>
| | |- |
| <th>ratio<br />
| | ! ratio |
| </th>
| | ! cents value |
| <th>cents value<br />
| | ! prime limit |
| </th>
| | |- |
| <th>prime limit<br />
| | | 18/13 = 54/39 |
| </th>
| | | 563.382 |
| </tr>
| | | 13 |
| <tr>
| | |- |
| <td>25/21<br />
| | | 43/31 |
| </td>
| | | 566.382 |
| <td>301.847<br />
| | | 43 |
| </td>
| | |- |
| <td>7<br />
| | | 25/18 |
| </td>
| | | 568.717 |
| </tr>
| | | 5 |
| <tr>
| | |- |
| <td>56/47<br />
| | | 32/23 |
| </td>
| | | 571.726 |
| <td>303.319<br />
| | | 23 |
| </td>
| | |- |
| <td>47<br />
| | | 39/28 |
| </td>
| | | 573.657 |
| </tr>
| | | 13 |
| <tr>
| | |- |
| <td>31/26<br />
| | | 46/33 |
| </td>
| | | 575.001 |
| <td>304.508<br />
| | | 23 |
| </td>
| | |- |
| <td>31<br />
| | | 60/43 |
| </td>
| | | 576.751 |
| </tr>
| | | 43 |
| <tr>
| | |} |
| <td>37/31<br />
| |
| </td>
| |
| <td>306.308<br />
| |
| </td>
| |
| <td>37<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>43/36<br />
| |
| </td>
| |
| <td>307.608<br />
| |
| </td>
| |
| <td>43<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>6/5 = 18/15 = 30/25 = 42/35 = 54/45<br />
| |
| </td>
| |
| <td>315.641<br />
| |
| </td>
| |
| <td>5<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>47/39<br />
| |
| </td>
| |
| <td>323.024<br />
| |
| </td>
| |
| <td>47<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>41/34<br />
| |
| </td>
| |
| <td>324.107<br />
| |
| </td>
| |
| <td>41<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>35/29<br />
| |
| </td>
| |
| <td>325.562<br />
| |
| </td>
| |
| <td>29<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>29/24<br />
| |
| </td>
| |
| <td>327.622<br />
| |
| </td>
| |
| <td>29<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>52/43<br />
| |
| </td>
| |
| <td>329.010<br />
| |
| </td>
| |
| <td>43<br />
| |
| </td>
| |
| </tr>
| |
| </table>
| |
|
| |
|
| <!-- ws:start:WikiTextHeadingRule:48:&lt;h2&gt; --><h2 id="toc24"><!-- ws:end:WikiTextHeadingRule:48 --> </h2>
| | ===Middle Tritones (577-623 cents)=== |
| <!-- ws:start:WikiTextHeadingRule:50:&lt;h2&gt; --><h2 id="toc25"><a name="x-Central or Zalzalian Thirds (formerly Neutral Thirds) (330-372 cents)"></a><!-- ws:end:WikiTextHeadingRule:50 -->Central or Zalzalian Thirds (formerly Neutral Thirds) (330-372 cents)</h2>
| |
| <!-- ws:start:WikiTextHeadingRule:52:&lt;h3&gt; --><h3 id="toc26"><a name="x-Central or Zalzalian Thirds (formerly Neutral Thirds) (330-372 cents)-Small Central Thirds (330-342 cents)"></a><!-- ws:end:WikiTextHeadingRule:52 -->Small Central Thirds (330-342 cents)</h3>
| |
|
| |
|
| |
|
| <table class="wiki_table">
| | {| class="wikitable" |
| <tr>
| | |- |
| <th>ratio<br />
| | ! ratio |
| </th>
| | ! cents value |
| <th>cents value<br />
| | ! prime limit |
| </th>
| | |- |
| <th>prime limit<br />
| | | 7/5 = 21/15 = 35/25 |
| </th>
| | | 582.512 |
| </tr>
| | | 7 |
| <tr>
| | |- |
| <td>23/19<br />
| | | 66/47 |
| </td>
| | | 587.766 |
| <td>330.761<br />
| | | 47 |
| </td>
| | |- |
| <td>23<br />
| | | 52/37 |
| </td>
| | | 589.184 |
| </tr>
| | | 37 |
| <tr>
| | |- |
| <td>40/33<br />
| | | 45/32 |
| </td>
| | | 590.224 |
| <td>333.041<br />
| | | 5 |
| </td>
| | |- |
| <td>11<br />
| | | 38/27 |
| </td>
| | | 591.648 |
| </tr>
| | | 19 |
| <tr>
| | |- |
| <td>17/14<br />
| | | 31/22 |
| </td>
| | | 593.718 |
| <td>336.130<br />
| | | 31 |
| </td>
| | |- |
| <td>17<br />
| | | 24/17 |
| </td>
| | | 597.000 |
| </tr>
| | | 17 |
| <tr>
| | |- |
| <td>45/37<br />
| | | 41/29 |
| </td>
| | | 599.485 |
| <td>338.880<br />
| | | 41 |
| </td>
| | |- |
| <td>37<br />
| | | 58/41 |
| </td>
| | | 600.515 |
| </tr>
| | | 41 |
| <tr>
| | |- |
| <td>28/23<br />
| | | 17/12 |
| </td>
| | | 603.000 |
| <td>340.552<br />
| | | 17 |
| </td>
| | |- |
| <td>23<br />
| | | 44/31 |
| </td>
| | | 606.282 |
| </tr>
| | | 31 |
| </table>
| | |- |
| | | 27/19 |
| | | 608.352 |
| | | 19 |
| | |- |
| | | 64/45 |
| | | 609.776 |
| | | 5 |
| | |- |
| | | 37/26 |
| | | 610.816 |
| | | 37 |
| | |- |
| | | 47/33 |
| | | 612.234 |
| | | 47 |
| | |- |
| | | 10/7 = 30/21 = 50/35 |
| | | 617.488 |
| | | 7 |
| | |} |
|
| |
|
| <!-- ws:start:WikiTextHeadingRule:54:&lt;h3&gt; --><h3 id="toc27"><a name="x-Central or Zalzalian Thirds (formerly Neutral Thirds) (330-372 cents)-Middle Central Thirds (342-360 cents)"></a><!-- ws:end:WikiTextHeadingRule:54 -->Middle Central Thirds (342-360 cents)</h3>
| | ===Large Tritones (623-640 cents)=== |
|
| |
|
| |
|
| <table class="wiki_table">
| | {| class="wikitable" |
| <tr>
| | |- |
| <th>ratio<br />
| | ! ratio |
| </th>
| | ! cents value |
| <th>cents value<br />
| | ! prime limit |
| </th>
| | |- |
| <th>prime limit<br />
| | | 43/30 |
| </th>
| | | 623.249 |
| </tr>
| | | 43 |
| <tr>
| | |- |
| <td>39/32<br />
| | | 33/23 |
| </td>
| | | 624.999 |
| <td>342.483<br />
| | | 23 |
| </td>
| | |- |
| <td>13<br />
| | | 56/39 |
| </td>
| | | 626.343 |
| </tr>
| | | 13 |
| <tr>
| | |- |
| <td>50/41<br />
| | | 23/16 |
| </td>
| | | 628.274 |
| <td>343.565<br />
| | | 23 |
| </td>
| | |- |
| <td>41<br />
| | | 36/25 |
| </td>
| | | 631.283 |
| </tr>
| | | 5 |
| <tr>
| | |- |
| <td>11/9 = 33/27<br />
| | | 62/43 |
| </td>
| | | 633.518 |
| <td>347.408<br />
| | | 43 |
| </td>
| | |- |
| <td>11<br />
| | | 13/9 = 39/27 |
| </td>
| | | 636.618 |
| </tr>
| | | 13 |
| <tr>
| | |- |
| <td>38/31<br />
| | | 68/47 |
| </td>
| | | 639.449 |
| <td>352.477<br />
| | | 47 |
| </td>
| | |} |
| <td>31<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>27/22<br />
| |
| </td>
| |
| <td>354.547<br />
| |
| </td>
| |
| <td>11<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>43/35<br />
| |
| </td>
| |
| <td>356.378<br />
| |
| </td>
| |
| <td>43<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>16/13 = 48/39<br />
| |
| </td>
| |
| <td>359.472<br />
| |
| </td>
| |
| <td>13<br />
| |
| </td>
| |
| </tr>
| |
| </table>
| |
|
| |
|
| <!-- ws:start:WikiTextHeadingRule:56:&lt;h3&gt; --><h3 id="toc28"><a name="x-Central or Zalzalian Thirds (formerly Neutral Thirds) (330-372 cents)-Large Central Thirds (360-372 cents)"></a><!-- ws:end:WikiTextHeadingRule:56 -->Large Central Thirds (360-372 cents)</h3>
| | ...to be continued... |
|
| |
|
| |
|
| <table class="wiki_table">
| | == See also == |
| <tr>
| |
| <th>ratio<br />
| |
| </th>
| |
| <th>cents value<br />
| |
| </th>
| |
| <th>prime limit<br />
| |
| </th>
| |
| </tr>
| |
| <tr>
| |
| <td>37/30<br />
| |
| </td>
| |
| <td>363.075<br />
| |
| </td>
| |
| <td>37<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>58/47<br />
| |
| </td>
| |
| <td>364.071<br />
| |
| </td>
| |
| <td>47<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>21/17<br />
| |
| </td>
| |
| <td>365.825<br />
| |
| </td>
| |
| <td>17<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>47/38<br />
| |
| </td>
| |
| <td>367.994<br />
| |
| </td>
| |
| <td>47<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>26/21<br />
| |
| </td>
| |
| <td>369.747<br />
| |
| </td>
| |
| <td>13<br />
| |
| </td>
| |
| </tr>
| |
| </table>
| |
|
| |
|
| <br />
| | * [[61-limit]] |
| <!-- ws:start:WikiTextHeadingRule:58:&lt;h2&gt; --><h2 id="toc29"><a name="x-Major Thirds (372-440 cents)"></a><!-- ws:end:WikiTextHeadingRule:58 -->Major Thirds (372-440 cents)</h2>
| |
| <!-- ws:start:WikiTextHeadingRule:60:&lt;h3&gt; --><h3 id="toc30"><a name="x-Major Thirds (372-440 cents)-Small Major Thirds (372-400 cents)"></a><!-- ws:end:WikiTextHeadingRule:60 -->Small Major Thirds (372-400 cents)</h3>
| |
|
| |
|
| |
|
| <table class="wiki_table">
| | [[Category:47-limit| ]] <!-- main article --> |
| <tr>
| | [[Category:Odd limit]] |
| <th>ratio<br />
| |
| </th>
| |
| <th>cents value<br />
| |
| </th>
| |
| <th>prime limit<br />
| |
| </th>
| |
| </tr>
| |
| <tr>
| |
| <td>31/25<br />
| |
| </td>
| |
| <td>372.408<br />
| |
| </td>
| |
| <td>31<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>36/29<br />
| |
| </td>
| |
| <td>374.333<br />
| |
| </td>
| |
| <td>29<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>41/33<br />
| |
| </td>
| |
| <td>375.789<br />
| |
| </td>
| |
| <td>41<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>46/37<br />
| |
| </td>
| |
| <td>376.930<br />
| |
| </td>
| |
| <td>37<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>56/45<br />
| |
| </td>
| |
| <td>378.602<br />
| |
| </td>
| |
| <td>7<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>5/4 = 15/12 = 25/20 = 35/28 = 45/36<br />
| |
| </td>
| |
| <td>386.314<br />
| |
| </td>
| |
| <td>5<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>54/43<br />
| |
| </td>
| |
| <td>394.347<br />
| |
| </td>
| |
| <td>43<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>44/35<br />
| |
| </td>
| |
| <td>396.178<br />
| |
| </td>
| |
| <td>11<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>39/31<br />
| |
| </td>
| |
| <td>397.447<br />
| |
| </td>
| |
| <td>31<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>34/27<br />
| |
| </td>
| |
| <td>399.090<br />
| |
| </td>
| |
| <td>17<br />
| |
| </td>
| |
| </tr>
| |
| </table>
| |
|
| |
|
| <br />
| | {{todo| add examples }} |
| ...to be continued...</body></html></pre></div>
| | [[Category:Lists of intervals]] |